In Section 5.1 we assumed that the restoring force F of
Chapter 10, Problem 10.1.137(choose chapter or problem)
In Section 5.1 we assumed that the restoring force F of the spring satisfied Hookes law F ks, where s is the elongation of the spring and k is a positive constant of proportionality. If we replace this assumption with the nonlinear law F ks3 , the new differential equation for damped motion of the hard spring becomes , where ks3 mg. The system is called overdamped when (0, 0) is a stable node and is called underdamped when (0, 0) is a stable spiral point. Find new conditions on m, k, and b that will lead to overdamping and underdamping.
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